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I have a 2-level LME which measures changes in an outcome variable across time, across individuals. Here, time points would be level 1, and the individuals would constitute level 2.

The individuals in my study are further classified into 2 groups. Once I have the random slopes for each individual, can I perform a t-test on the random slopes of the two groups to determine if the rates of change of the outcome variable with time are different between the two groups?

I originally thought of adding the group variable with 2 groups as the third level in my model, but a level with only 2 groups doesn't seem right.

romantic_cockroach
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I would not perform a t-test on random effect estimates. Such an approach would not be taking into account how those parameters were estimated, but rather treats them as observed quantities. The theoretical guarantees in this case would be questionable.

Your hesitancy to add a random effect with a low number of groups is shared by many statisticians (e.g. see here and here and for counter arguments consider Gelman)

In such a case you can always add the group effect as a fixed effect.

Regardless of which route you take I would prefer to fit the model in a Bayesian context rather than rely on frequentist asymptotics and p-values which are not well established for mixed effects models.

bdeonovic
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